Modeling Zero-Inflated Correlated Dental Data through Gaussian Copulas and Approximate Bayesian Computation

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Summary

The study proposes a zero-inflated spatio-temporal correlated count data model using a Negative Binomial hurdle model and a Gaussian copula with a Simultaneous Autoregressive (SAR) model. The model is applied to the Iowa Fluoride Study (IFS) data to investigate the associations between dental caries and various risk and protective factors.

Highlights

• The model accounts for zero-inflation and spatio-temporal correlation in count data.
• A Gaussian copula is used to specify dependence using a SAR model with multiple adjacency relationships.
• The model is applied to the IFS data to investigate dental caries associations.
• The study uses Approximate Bayesian Computation (ABC) for posterior inference.
• The model is compared to alternative marginal model specifications.
• The study investigates the sensitivity of the model fit to the dependence model specification.
• The results show that the model performs well in terms of estimation and coverage.

Key Insights

• The proposed model is able to capture the complex correlation structure in the IFS data, including the effects of dental visits, brushing frequency, and sugary beverage consumption on dental caries.
• The use of a Gaussian copula with a SAR model allows for flexible modeling of the dependence structure, including multiple types of adjacency relationships.
• The ABC approach is effective for posterior inference in this complex model, allowing for the estimation of model parameters and the evaluation of model performance.
• The comparison to alternative marginal model specifications highlights the importance of accounting for zero-inflation and over-dispersion in the data.
• The sensitivity analysis shows that the model fit is robust to different dependence model specifications, but that the true data-generating model is the best performing model.
• The results of the study have implications for the analysis of complex correlated count data in various fields, including epidemiology and public health.
• The study demonstrates the importance of using advanced statistical models and computational methods to analyze complex data and gain insights into underlying relationships and mechanisms.

Mindmap

Citation

Mukherjee, A., Gaskins, J. T., Sarkar, S., Levy, S., & Datta, S. (2024). Modeling Zero-Inflated Correlated Dental Data through Gaussian Copulas and Approximate Bayesian Computation (Version 2). arXiv. https://doi.org/10.48550/ARXIV.2410.13949